Loss Distribution Calculation System, Loss Distribution Calculation Method and Loss Distribution Calculation-Use Program

1. A loss distribution calculation system, comprising: a frequency distribution/scale distribution input section configured to input information about a frequency distribution and a scale distribution; a scale distribution discretization section configured to perform either one or both of upside and downside discretizations for the input scale distribution; a sub-composite distribution calculation section configured to calculate, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all the events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; an accuracy calculation section configured to calculate: upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and an accuracy of the approximate value; and a loss distribution output section configured to output information about the approximate value of the loss distribution function, with guaranteed accuracy, represented by information about the calculated accuracy, wherein: each of the frequency distribution/scale distribution input section, the scale distribution discretization section, the sub-composite distribution calculation section, the accuracy calculation section, and the loss distribution output section is implemented using hardware; the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution.

2. The loss distribution calculation system according to claim 1 , wherein if the calculated accuracy has not reached a desired level, then the sub-composite distribution calculation section enlarges a range of a portion where a probability value is calculated in the division of the all events and calculates again either one or both of the upside and downside sub-composite distributions, and when the calculated accuracy has reached a desired level, the loss distribution output section outputs the information about the approximate value of the loss distribution function with guaranteed accuracy represented by information about the calculated accuracy.

3. The loss distribution calculation system according to claim 1 , further comprising: a frequency distribution accumulation section in which information about the frequency distribution input by the frequency distribution/scale distribution input section is accumulated; a scale distribution accumulation section in which information about the scale distribution input by the frequency distribution/scale distribution input section is accumulated; a discretized scale distribution accumulation section in which the scale distribution for which either one or both of the upside and downside discretizations are performed by the scale distribution discretization section is accumulated; and a sub-composite distribution accumulation section in which the upside or downside sub-composite distribution calculated by either one or both of the sub-composite distribution calculation sections are accumulated, wherein each of the frequency distribution accumulation section, the scale distribution accumulation section, the discretized scale distribution accumulation section, and the sub-composite distribution accumulation section is implemented using hardware.

4. The loss distribution calculation system according to claim 1 , wherein a computer functions as the scale distribution discretization section, the sub-composite distribution calculation section and the accuracy calculation section.

5. A loss distribution calculation method of a loss distribution calculation system, the method comprising: inputting, by a processor, information about a frequency distribution and a scale distribution; performing, by the processor, either one or both of upside and downside discretizations for the input scale distribution; calculating, by the processor, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; calculating, by the processor, upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, calculates a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and calculates an accuracy of the approximate value; and outputting, by the processor, information about the approximate value of the loss distribution function with guaranteed accuracy, represented by information about the calculated accuracy; the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution.

6. The loss distribution calculation method according to claim 5 , further comprising: if the calculated accuracy has not reached a desired level, then enlarging, by the processor, a range of a portion where a probability value is calculated in the division of the all events and calculating, by the processor, again either one or both of the upside and downside sub-composite distributions, and when the calculated accuracy has reached a desired level, outputting by the processor, the information about the approximate value of the loss distribution function with guaranteed accuracy represented by information about the calculated accuracy.

7. A non-transitory computer-readable medium, on which a program is recorded, said program causes a computer to perform a loss distribution calculation method comprising: inputting information about a frequency distribution and a scale distribution; performing either one or both of upside and downside discretizations for the input scale distribution; calculating, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; calculating upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, calculates a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and calculates an accuracy of the approximate value; and outputting information about the approximate value of the loss distribution function with guaranteed accuracy represented by information about the calculated accuracy; wherein: the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution.

8. The non-transitory computer-readable medium according to claim 7 , wherein the method further comprises: if the calculated accuracy has not reached a desired level, then enlarging a range of a portion where a probability value is calculated in the division of the all events and calculating again either one or both of the upside and downside sub-composite distributions, and when the calculated accuracy has reached a desired level, outputting the information about the approximate value of the loss distribution function with guaranteed accuracy represented by information about the calculated accuracy.